Nested weighted limit-average automata of bounded width

K. Chatterjee, T.A. Henzinger, J. Otop, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016.

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Conference Paper | Published | English
Series Title
LIPIcs
Abstract
While weighted automata provide a natural framework to express quantitative properties, many basic properties like average response time cannot be expressed with weighted automata. Nested weighted automata extend weighted automata and consist of a master automaton and a set of slave automata that are invoked by the master automaton. Nested weighted automata are strictly more expressive than weighted automata (e.g., average response time can be expressed with nested weighted automata), but the basic decision questions have higher complexity (e.g., for deterministic automata, the emptiness question for nested weighted automata is PSPACE-hard, whereas the corresponding complexity for weighted automata is PTIME). We consider a natural subclass of nested weighted automata where at any point at most a bounded number k of slave automata can be active. We focus on automata whose master value function is the limit average. We show that these nested weighted automata with bounded width are strictly more expressive than weighted automata (e.g., average response time with no overlapping requests can be expressed with bound k=1, but not with non-nested weighted automata). We show that the complexity of the basic decision problems (i.e., emptiness and universality) for the subclass with k constant matches the complexity for weighted automata. Moreover, when k is part of the input given in unary we establish PSPACE-completeness.
Publishing Year
Date Published
2016-08-01
Acknowledgement
This research was supported in part by the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award), ERC Start grant (279307: Graph Games), Vienna Science and Technology Fund (WWTF) through project ICT15-003 and by the National Science Centre (NCN), Poland under grant 2014/15/D/ST6/04543.
Volume
58
Article Number
24
Conference
MFCS: Mathematical Foundations of Computer Science (SG)
Conference Location
Krakow; Poland
Conference Date
2016-08-22 – 2016-08-26
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Cite this

Chatterjee K, Henzinger TA, Otop J. Nested weighted limit-average automata of bounded width. In: Vol 58. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2016. doi:10.4230/LIPIcs.MFCS.2016.24
Chatterjee, K., Henzinger, T. A., & Otop, J. (2016). Nested weighted limit-average automata of bounded width (Vol. 58). Presented at the MFCS: Mathematical Foundations of Computer Science (SG), Krakow; Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.MFCS.2016.24
Chatterjee, Krishnendu, Thomas A Henzinger, and Jan Otop. “Nested Weighted Limit-Average Automata of Bounded Width,” Vol. 58. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. https://doi.org/10.4230/LIPIcs.MFCS.2016.24.
K. Chatterjee, T. A. Henzinger, and J. Otop, “Nested weighted limit-average automata of bounded width,” presented at the MFCS: Mathematical Foundations of Computer Science (SG), Krakow; Poland, 2016, vol. 58.
Chatterjee K, Henzinger TA, Otop J. 2016. Nested weighted limit-average automata of bounded width. MFCS: Mathematical Foundations of Computer Science (SG), LIPIcs, vol. 58.
Chatterjee, Krishnendu, et al. Nested Weighted Limit-Average Automata of Bounded Width. Vol. 58, 24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016, doi:10.4230/LIPIcs.MFCS.2016.24.
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